A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL= 1 and MPK= 1. Let w = 1 and r = 1 be the prices of labor and capital, respectively.
a) Find the equation for the firm?s long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and r = 1.
b) Find the solution to the firm?s short-run cost minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5), and w = 1 and r = 1. Derive the equation for the firm?s short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve.
c) How do the graphs of the short-run and long-run total cost curves change when w = 1 and r = 2?
d) How do the graphs of the short-run and long-run total cost curves change when w = 2 and r = 1?